Witnessing Bell violations through probabilistic negativity

TL;DR

This paper introduces a quasiprobabilistic framework for Bell inequalities, linking negativity in hidden-variable models to quantum violations, and provides an analytic measure of negativity needed for Bell violation.

Contribution

It presents a novel approach by relaxing positivity in hidden-variable models, deriving Bell inequalities based on negativity, and quantifying negativity required for quantum violations.

Findings

Derived quasiprobabilistic Bell inequalities with negativity-based bounds

Provided an analytic expression for negativity needed to violate CHSH inequality

Linked negativity witness to the extent of Bell violation

Abstract

Bell's theorem shows that no hidden-variable model can explain the measurement statistics of a quantum system shared between two parties, thus ruling out a classical (local) understanding of nature. In this work we demonstrate that by relaxing the positivity restriction in the hidden-variable probability distribution it is possible to derive quasiprobabilistic Bell inequalities whose sharp upper bound is written in terms of a negativity witness of said distribution. This provides an analytic solution for the amount of negativity necessary to violate the CHSH inequality by an arbitrary amount, therefore revealing the amount of negativity required to emulate the quantum statistics in a Bell test.